Details

Time bar (total: 5.8s)

sample22.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0117
1117

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
20×pow1
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
4×add-exp-log sqrt-div associate-/r* add-cbrt-cube
3×sqrt-prod
2×log-div flip3-+ div-sub flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num div-inv
Counts
2 → 63
Calls
2 calls:
7.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms
(sqrt (+ (* re re) (* im im)))

series180.0ms

Counts
2 → 6
Calls
2 calls:
145.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify122.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 4 (116.0ms)

IterNodesCost
0221664
1556631
21309628
34047628
45001627

prune191.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.4b
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
107×add-sqr-sqrt
78×sqrt-prod
66×*-un-lft-identity
61×log-pow
60×add-cube-cbrt
52×pow1
46×associate-*r*
27×add-exp-log
25×associate-*l*
17×add-cbrt-cube
16×sqrt-pow1 pow1/2
15×unswap-sqr
9×div-exp
8×prod-exp
7×associate-/r*
6×associate-/l*
5×cbrt-undiv
4×sqrt-div cbrt-unprod
3×div-inv add-log-exp
2×log-div rec-exp flip3-+ 1-exp div-sub flip-+
1×frac-times rem-sqrt-square frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 194
Calls
3 calls:
28.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
8.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series381.0ms

Counts
3 → 9
Calls
3 calls:
139.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
204.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06132721
124602427
250012325

prune417.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.3b
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.9b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
45×add-cube-cbrt
41×sqrt-prod
30×log-prod
25×pow-unpow associate-*l*
24×unpow-prod-down
16×add-exp-log
15×pow1
10×distribute-rgt-in distribute-lft-in
9×add-cbrt-cube
8×log-pow
5×unswap-sqr
4×associate-*r* prod-exp add-log-exp sqr-pow
3×pow-pow rem-log-exp
2×pow-to-exp sqrt-pow1 pow1/2 sqrt-div div-exp pow-exp cbrt-unprod div-inv
1×cbrt-undiv rem-sqrt-square rec-exp flip3-+ 1-exp pow-prod-down associate-*l/ *-commutative sqrt-pow2 flip-+
Counts
4 → 151
Calls
4 calls:
5.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
14.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
7.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms
(sqrt (+ (* re re) (* im im)))

series1.0s

Counts
4 → 12
Calls
4 calls:
305.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
354.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
339.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05582291
123431895
250021744

prune419.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1/2 (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
0.3b
(* (/ 1/2 (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
50×associate-*l*
46×times-frac
44×add-cube-cbrt *-un-lft-identity sqrt-prod
24×log-prod
20×pow1
14×add-exp-log add-cbrt-cube
12×distribute-rgt-in distribute-lft-in associate-*r* log-pow
6×unswap-sqr
4×sqrt-pow1 pow1/2 sqrt-div prod-exp cbrt-unprod add-log-exp
2×cbrt-undiv rem-sqrt-square flip3-+ div-exp pow-prod-down associate-*l/ *-commutative flip-+ div-inv
Counts
4 → 150
Calls
4 calls:
13.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
13.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
244.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
35.0ms
(sqrt (+ (* re re) (* im im)))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
03401818
110191682
235591632
350011632

prune499.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.4b

regimes874.0ms

Accuracy

57.1% (10.5b remaining)

Error of 17.6b against oracle of 7.1b and baseline of 31.6b

bsearch162.0ms

Steps
ItersRangePoint
8
1.489929931039939e+45
1.7374334306820677e+49
1.5839519867424625e+49
8
8.759955465341852e-197
9.415971551391981e-194
3.6483869476023075e-196
8
4.592090908020972e-292
2.209994737107717e-288
1.2556355458008622e-289
6
-6.667724969208778e+44
-4.3606823432867463e+43
-6.122290979091217e+44

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06383
16383

end0.0ms

sample499.0ms

Algorithm
intervals
Results
352.0ms8000×body80valid